0
What else can I help you with?
What is the exact value of cos theta if csc theta -4 with theta in quadrant III?
csc θ = 1/sin θ → sin θ = -1/4 cos² θ + sin² θ = 1 → cos θ = ± √(1 - sin² θ) = ± √(1 - ¼²) = ± √(1- 1/16) = ± √(15/16) = ± (√15)/4 In Quadrant III both cos and sin are negative → cos θ= -(√15)/4
Is it possible for sin theta cos theta and tan theta to all be negative for the same value of theta?
No, they cannot all be negative and retain the same value for theta, as is shown with the four quadrants and their trigonemtric properties. For example, in the first quadrant (0
If sin theta equals 3/4 and theta is in quadrant II what is the value of tan theta?
0.75
If sin is negative that make cosecant negative as well?
Yes: cosecant = 1/sine If sine negative, 1/sine is negative → cosecant is negative.
What is the derivative of cos x?
d/dx(-cosx)=--sinx=sinx
Why is the tangent positive on quadrant III?
The tangent function is equal to the sine divided by the cosine. In quadrant III, both sin and cos are negative - and a negative divided by another negative is positive. Thus it follows that the tangent is positive in QIII.
Tan equals 0.3421 sin equals 0.3237 Which quadrant does it terminate?
The value of tan and sin is positive so you must search quadrant that tan and sin value is positive. The only quadrant fill that qualification is Quadrant 1.
How could you tell if tan is negative or positive in a quadrant Example in quadrant II cos - and sin is plus but what is tan?
There's a mnemonic for this: All Students Take Calculus. Starting in the first quadrant, and moving counterclockwise until the last, give each quadrant the first letter of thos words in order. A represents all 3, s represents sine, t represents tangent, and c represents cosine. If the letter appears in a quadrant, it is positive there. If not, it is negative there.In quadrant 2, only sine is positive.
Is Sin a negative function or positive?
negative
What is sin 210?
The sine of 210 degrees is equal to -1/2. This value can be derived from the unit circle, where 210 degrees is in the third quadrant, where sine values are negative. Specifically, sin(210°) corresponds to sin(210° - 180°) = sin(30°), and since sine is negative in the third quadrant, sin(210°) = -sin(30°) = -1/2.
If costheta -.444 with theta in quadrant 2 find sintheta?
Since theta is in the second quadrant, sin(theta) is positive. sin2(theta) = 1 - cos2(theta) = 0.803 So sin(theta) = +sqrt(0.803) = 0.896.
Why does sin negative theta equal sin positive theta?
It is not! So the question is irrelevant.
How do you solve sine theta equal to negative one half?
Consider angles in standard position, and note that for the equation sin θ = 0.5, the angle in the first quadrant is θ = 30° The sin function is positive in quadrants I and II, and negative in quadrants III and IV, so there are two basic answers, one in quadrant III and another in quadrant IV. In quadrant III, the angle is 180° + 30° = 210° In quadrant IV, the angle is 360° - 30° = 330° Of course, this is a wave function so there are an infinite number of answers. You can add full circles (i.e. multiples of 360°) to either of these answers to get more answers. In quadrant III, the angles are 210°, 570°, 930°, ... In quadrant IV, the angles are 330°, 690°, 1050°, ...
Why sin positive in 1st quadrant?
That follows from the definition of the sine function. There are several equivalent definitions, but for example, it can be defined as the y-coordinate of the unit circle, as a function of the angle. You start measuring the circle from coordinates (1,0), and continue counterclockwise. _________________________________________ This is because both sin definition is the length of line opposite to the angle divided by the angle side line. Since both lines are positive in the first quadrant, the sin value is positive.
What is tan theta in terms of sin theta in quadrant II?
tan = sin/cos Now cos2 = 1 - sin2 so cos = +/- sqrt(1 - sin2) In the second quadrant, cos is negative, so cos = - sqrt(1 - sin2) So that tan = sin/[-sqrt(1 - sin2)] or -sin/sqrt(1 - sin2)
Tan equals 0.3421 sin equals 3237 Which quadrant does it terminate?
Assuming sin equals 0.3237, the angle is in quadrant I.
What is the exact value of cos theta if csc theta -4 with theta in quadrant III?
csc θ = 1/sin θ → sin θ = -1/4 cos² θ + sin² θ = 1 → cos θ = ± √(1 - sin² θ) = ± √(1 - ¼²) = ± √(1- 1/16) = ± √(15/16) = ± (√15)/4 In Quadrant III both cos and sin are negative → cos θ= -(√15)/4
